I am sorry that you are experiencing such a dilemma.
A good rule of thumb is to send an email to your manager after a one-on-one meeting, outlining the salient points of discussion. For example:
Good Afternoon NM,
Thank you for taking the time to meet with me today. I feel that we discussed some important issues and I am encouraged by the feedback that you gave me.
I am looking forward to a full time position, as we discussed today. I realize that it can take some time for an opening to become available on this unit. Thank you for your support in letting me know that I am next in line when a full time position opens.
Since you are putting your discussion in writing, you are holding the NM accountable for their promises. If the NM disagrees with your interpretation of the meeting, they will have no choice but to either respond to your email or talk to you in person. You are in effect, making them outline specific points as to why you were passed over. You can then respond in another email that addresses the reasons why you were passed over.
You are creating a written documentation of your discussions, which then removes the "he said/she said" factor when questions arise.
This sort of documentation will also give you a leg up when your NM lists specific things that you need to work on. From that point, you can develop a measurable plan of action to work toward in getting a full time position.
The key is to have a written record of your meetings with your NM.
I wish you only the best!